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Ksivusya [100]
3 years ago
10

Find the rectangle coordinates of (5,30 degrees)

Mathematics
1 answer:
balu736 [363]3 years ago
6 0
I’m hanks I need to see the rectangle for this
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Find the average value of f over region
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D is a right triangle with base length 1 and height 8, so the area of D is \dfrac12(1)(8)=4.

The average value of f(x,y) over D is given by the ratio

\dfrac{\displaystyle\iint_Df(x,y)\,\mathrm dA}{\displaystyle\iint_D\mathrm dA}

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\displaystyle\frac74\iint_Dxy\,\mathrm dA

In the x,y-plane, we can describe the region D as all points (x,y) that lie between the lines y=0 and y=8x (the lines which coincide with the triangle's base and hypotenuse, respectively), taking 0\le x\le1. So, the integral is given by, and evaluates to,

\displaystyle\frac74\int_{x=0}^{x=1}\int_{y=0}^{y=8x}xy\,\mathrm dy\,\mathrm dx=\frac78\int_{x=0}^{x=1}xy^2\bigg|_{y=0}^{y=8x}\,\mathrm dx
=\displaystyle56\int_{x=0}^{x=1}x^3\,\mathrm dx
=14x^4\bigg|_{x=0}^{x=1}
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How are the ratios 3:6 and 9:18 related?
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